Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B

Percentage Accurate: 75.3% → 90.3%

Time: 19.1s

Alternatives: 17

Speedup: 0.6×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 75.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_3 := 1 + \left(a + b \cdot \frac{y}{t}\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t\_3}\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;t\_2 \leq 10^{+275}:\\ \;\;\;\;\frac{t\_1}{\frac{1}{t} \cdot \left(y \cdot b\right) + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_3} + \frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ (/ (* y b) t) (+ a 1.0))))
        (t_3 (+ 1.0 (+ a (* b (/ y t))))))
   (if (<= t_2 (- INFINITY))
     (* (/ y t) (/ z t_3))
     (if (<= t_2 -2e-308)
       t_2
       (if (<= t_2 0.0)
         (/ (+ z (* t (/ x y))) b)
         (if (<= t_2 1e+275)
           (/ t_1 (+ (* (/ 1.0 t) (* y b)) (+ a 1.0)))
           (+ (/ x t_3) (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double t_3 = 1.0 + (a + (b * (y / t)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / t_3);
	} else if (t_2 <= -2e-308) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_2 <= 1e+275) {
		tmp = t_1 / (((1.0 / t) * (y * b)) + (a + 1.0));
	} else {
		tmp = (x / t_3) + (z / b);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double t_3 = 1.0 + (a + (b * (y / t)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / t_3);
	} else if (t_2 <= -2e-308) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_2 <= 1e+275) {
		tmp = t_1 / (((1.0 / t) * (y * b)) + (a + 1.0));
	} else {
		tmp = (x / t_3) + (z / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / (((y * b) / t) + (a + 1.0))
	t_3 = 1.0 + (a + (b * (y / t)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (y / t) * (z / t_3)
	elif t_2 <= -2e-308:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (z + (t * (x / y))) / b
	elif t_2 <= 1e+275:
		tmp = t_1 / (((1.0 / t) * (y * b)) + (a + 1.0))
	else:
		tmp = (x / t_3) + (z / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_3 = Float64(1.0 + Float64(a + Float64(b * Float64(y / t))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / t_3));
	elseif (t_2 <= -2e-308)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	elseif (t_2 <= 1e+275)
		tmp = Float64(t_1 / Float64(Float64(Float64(1.0 / t) * Float64(y * b)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(x / t_3) + Float64(z / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	t_3 = 1.0 + (a + (b * (y / t)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (y / t) * (z / t_3);
	elseif (t_2 <= -2e-308)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (z + (t * (x / y))) / b;
	elseif (t_2 <= 1e+275)
		tmp = t_1 / (((1.0 / t) * (y * b)) + (a + 1.0));
	else
		tmp = (x / t_3) + (z / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-308], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$2, 1e+275], N[(t$95$1 / N[(N[(N[(1.0 / t), $MachinePrecision] * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t$95$3), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0

   1. Initial program 33.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 52.8%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 52.8%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 52.8%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 52.7%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 52.8%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 52.8%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in x around 0 61.9%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}} \]
   8. Step-by-step derivation

      1. times-frac 94.1%

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]

      2. associate-/l* 84.1%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} \]

   9. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)}} \]

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.9999999999999998e-308

   1. Initial program 99.7%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   if -1.9999999999999998e-308 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 50.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 54.7%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 63.6%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 63.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 55.1%

      \[\leadsto \color{blue}{\frac{t \cdot \left(x + \frac{y \cdot z}{t}\right)}{b \cdot y}} \]

   6. Taylor expanded in t around 0 63.1%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t \cdot x}{b \cdot y}} \]
   7. Step-by-step derivation

      1. times-frac 73.1%

         \[\leadsto \frac{z}{b} + \color{blue}{\frac{t}{b} \cdot \frac{x}{y}} \]

   8. Simplified 73.1%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}} \]

   9. Taylor expanded in b around 0 70.2%

      \[\leadsto \color{blue}{\frac{z + \frac{t \cdot x}{y}}{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 75.3%

          \[\leadsto \frac{z + \color{blue}{t \cdot \frac{x}{y}}}{b} \]

   11. Simplified 75.3%

       \[\leadsto \color{blue}{\frac{z + t \cdot \frac{x}{y}}{b}} \]

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999996e274

   1. Initial program 99.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.3%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\frac{1}{\frac{t}{y \cdot b}}}} \]

      2. associate-/r/ 99.4%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\frac{1}{t} \cdot \left(y \cdot b\right)}} \]

   4. Applied egg-rr 99.4%

      \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\frac{1}{t} \cdot \left(y \cdot b\right)}} \]

   if 9.9999999999999996e274 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 6.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 17.5%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 40.4%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 40.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 40.5%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 40.5%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 40.5%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in x around 0 19.3%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}} \]
   8. Step-by-step derivation

      1. +-commutative 19.3%

         \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]

      2. times-frac 30.1%

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{b \cdot y}{t}\right)}} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      3. associate-/l* 42.5%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      4. associate-/l* 50.2%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} \]

   9. Simplified 50.2%

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}} \]

   10. Taylor expanded in y around inf 82.3%

       \[\leadsto \color{blue}{\frac{z}{b}} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-308}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+275}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{1}{t} \cdot \left(y \cdot b\right) + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_2 := 1 + \left(a + b \cdot \frac{y}{t}\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t\_2}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-308}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;t\_1 \leq 10^{+275}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_2} + \frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0))))
        (t_2 (+ 1.0 (+ a (* b (/ y t))))))
   (if (<= t_1 (- INFINITY))
     (* (/ y t) (/ z t_2))
     (if (<= t_1 -2e-308)
       t_1
       (if (<= t_1 0.0)
         (/ (+ z (* t (/ x y))) b)
         (if (<= t_1 1e+275) t_1 (+ (/ x t_2) (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = 1.0 + (a + (b * (y / t)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / t_2);
	} else if (t_1 <= -2e-308) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_1 <= 1e+275) {
		tmp = t_1;
	} else {
		tmp = (x / t_2) + (z / b);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = 1.0 + (a + (b * (y / t)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / t_2);
	} else if (t_1 <= -2e-308) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_1 <= 1e+275) {
		tmp = t_1;
	} else {
		tmp = (x / t_2) + (z / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	t_2 = 1.0 + (a + (b * (y / t)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y / t) * (z / t_2)
	elif t_1 <= -2e-308:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (z + (t * (x / y))) / b
	elif t_1 <= 1e+275:
		tmp = t_1
	else:
		tmp = (x / t_2) + (z / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_2 = Float64(1.0 + Float64(a + Float64(b * Float64(y / t))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / t_2));
	elseif (t_1 <= -2e-308)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	elseif (t_1 <= 1e+275)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t_2) + Float64(z / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	t_2 = 1.0 + (a + (b * (y / t)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y / t) * (z / t_2);
	elseif (t_1 <= -2e-308)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (z + (t * (x / y))) / b;
	elseif (t_1 <= 1e+275)
		tmp = t_1;
	else
		tmp = (x / t_2) + (z / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-308], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 1e+275], t$95$1, N[(N[(x / t$95$2), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0

   1. Initial program 33.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 52.8%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 52.8%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 52.8%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 52.7%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 52.8%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 52.8%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in x around 0 61.9%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}} \]
   8. Step-by-step derivation

      1. times-frac 94.1%

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]

      2. associate-/l* 84.1%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} \]

   9. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)}} \]

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.9999999999999998e-308 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999996e274

   1. Initial program 99.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   if -1.9999999999999998e-308 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 50.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 54.7%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 63.6%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 63.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 55.1%

      \[\leadsto \color{blue}{\frac{t \cdot \left(x + \frac{y \cdot z}{t}\right)}{b \cdot y}} \]

   6. Taylor expanded in t around 0 63.1%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t \cdot x}{b \cdot y}} \]
   7. Step-by-step derivation

      1. times-frac 73.1%

         \[\leadsto \frac{z}{b} + \color{blue}{\frac{t}{b} \cdot \frac{x}{y}} \]

   8. Simplified 73.1%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}} \]

   9. Taylor expanded in b around 0 70.2%

      \[\leadsto \color{blue}{\frac{z + \frac{t \cdot x}{y}}{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 75.3%

          \[\leadsto \frac{z + \color{blue}{t \cdot \frac{x}{y}}}{b} \]

   11. Simplified 75.3%

       \[\leadsto \color{blue}{\frac{z + t \cdot \frac{x}{y}}{b}} \]

   if 9.9999999999999996e274 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 6.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 17.5%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 40.4%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 40.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 40.5%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 40.5%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 40.5%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in x around 0 19.3%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}} \]
   8. Step-by-step derivation

      1. +-commutative 19.3%

         \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]

      2. times-frac 30.1%

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{b \cdot y}{t}\right)}} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      3. associate-/l* 42.5%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      4. associate-/l* 50.2%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} \]

   9. Simplified 50.2%

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}} \]

   10. Taylor expanded in y around inf 82.3%

       \[\leadsto \color{blue}{\frac{z}{b}} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-308}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+275}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_3 := 1 + \left(a + b \cdot \frac{y}{t}\right)\\ t_4 := \frac{x}{t\_3}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-308}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t\_3} + t\_4\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;t\_2 \leq 10^{+275}:\\ \;\;\;\;\frac{t\_1}{\frac{1}{t} \cdot \left(y \cdot b\right) + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_4 + \frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ (/ (* y b) t) (+ a 1.0))))
        (t_3 (+ 1.0 (+ a (* b (/ y t)))))
        (t_4 (/ x t_3)))
   (if (<= t_2 -2e-308)
     (+ (* (/ y t) (/ z t_3)) t_4)
     (if (<= t_2 0.0)
       (/ (+ z (* t (/ x y))) b)
       (if (<= t_2 1e+275)
         (/ t_1 (+ (* (/ 1.0 t) (* y b)) (+ a 1.0)))
         (+ t_4 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double t_3 = 1.0 + (a + (b * (y / t)));
	double t_4 = x / t_3;
	double tmp;
	if (t_2 <= -2e-308) {
		tmp = ((y / t) * (z / t_3)) + t_4;
	} else if (t_2 <= 0.0) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_2 <= 1e+275) {
		tmp = t_1 / (((1.0 / t) * (y * b)) + (a + 1.0));
	} else {
		tmp = t_4 + (z / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    t_2 = t_1 / (((y * b) / t) + (a + 1.0d0))
    t_3 = 1.0d0 + (a + (b * (y / t)))
    t_4 = x / t_3
    if (t_2 <= (-2d-308)) then
        tmp = ((y / t) * (z / t_3)) + t_4
    else if (t_2 <= 0.0d0) then
        tmp = (z + (t * (x / y))) / b
    else if (t_2 <= 1d+275) then
        tmp = t_1 / (((1.0d0 / t) * (y * b)) + (a + 1.0d0))
    else
        tmp = t_4 + (z / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double t_3 = 1.0 + (a + (b * (y / t)));
	double t_4 = x / t_3;
	double tmp;
	if (t_2 <= -2e-308) {
		tmp = ((y / t) * (z / t_3)) + t_4;
	} else if (t_2 <= 0.0) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_2 <= 1e+275) {
		tmp = t_1 / (((1.0 / t) * (y * b)) + (a + 1.0));
	} else {
		tmp = t_4 + (z / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / (((y * b) / t) + (a + 1.0))
	t_3 = 1.0 + (a + (b * (y / t)))
	t_4 = x / t_3
	tmp = 0
	if t_2 <= -2e-308:
		tmp = ((y / t) * (z / t_3)) + t_4
	elif t_2 <= 0.0:
		tmp = (z + (t * (x / y))) / b
	elif t_2 <= 1e+275:
		tmp = t_1 / (((1.0 / t) * (y * b)) + (a + 1.0))
	else:
		tmp = t_4 + (z / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_3 = Float64(1.0 + Float64(a + Float64(b * Float64(y / t))))
	t_4 = Float64(x / t_3)
	tmp = 0.0
	if (t_2 <= -2e-308)
		tmp = Float64(Float64(Float64(y / t) * Float64(z / t_3)) + t_4);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	elseif (t_2 <= 1e+275)
		tmp = Float64(t_1 / Float64(Float64(Float64(1.0 / t) * Float64(y * b)) + Float64(a + 1.0)));
	else
		tmp = Float64(t_4 + Float64(z / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	t_3 = 1.0 + (a + (b * (y / t)));
	t_4 = x / t_3;
	tmp = 0.0;
	if (t_2 <= -2e-308)
		tmp = ((y / t) * (z / t_3)) + t_4;
	elseif (t_2 <= 0.0)
		tmp = (z + (t * (x / y))) / b;
	elseif (t_2 <= 1e+275)
		tmp = t_1 / (((1.0 / t) * (y * b)) + (a + 1.0));
	else
		tmp = t_4 + (z / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x / t$95$3), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-308], N[(N[(N[(y / t), $MachinePrecision] * N[(z / t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$2, 1e+275], N[(t$95$1 / N[(N[(N[(1.0 / t), $MachinePrecision] * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$4 + N[(z / b), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.9999999999999998e-308

   1. Initial program 91.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 91.1%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 89.8%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 89.7%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 89.9%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 89.9%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in x around 0 94.8%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}} \]
   8. Step-by-step derivation

      1. +-commutative 94.8%

         \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]

      2. times-frac 95.9%

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{b \cdot y}{t}\right)}} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      3. associate-/l* 94.6%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      4. associate-/l* 94.6%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} \]

   9. Simplified 94.6%

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}} \]

   if -1.9999999999999998e-308 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 50.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 54.7%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 63.6%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 63.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 55.1%

      \[\leadsto \color{blue}{\frac{t \cdot \left(x + \frac{y \cdot z}{t}\right)}{b \cdot y}} \]

   6. Taylor expanded in t around 0 63.1%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t \cdot x}{b \cdot y}} \]
   7. Step-by-step derivation

      1. times-frac 73.1%

         \[\leadsto \frac{z}{b} + \color{blue}{\frac{t}{b} \cdot \frac{x}{y}} \]

   8. Simplified 73.1%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}} \]

   9. Taylor expanded in b around 0 70.2%

      \[\leadsto \color{blue}{\frac{z + \frac{t \cdot x}{y}}{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 75.3%

          \[\leadsto \frac{z + \color{blue}{t \cdot \frac{x}{y}}}{b} \]

   11. Simplified 75.3%

       \[\leadsto \color{blue}{\frac{z + t \cdot \frac{x}{y}}{b}} \]

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999996e274

   1. Initial program 99.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.3%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\frac{1}{\frac{t}{y \cdot b}}}} \]

      2. associate-/r/ 99.4%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\frac{1}{t} \cdot \left(y \cdot b\right)}} \]

   4. Applied egg-rr 99.4%

      \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\frac{1}{t} \cdot \left(y \cdot b\right)}} \]

   if 9.9999999999999996e274 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 6.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 17.5%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 40.4%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 40.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 40.5%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 40.5%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 40.5%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in x around 0 19.3%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}} \]
   8. Step-by-step derivation

      1. +-commutative 19.3%

         \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]

      2. times-frac 30.1%

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{b \cdot y}{t}\right)}} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      3. associate-/l* 42.5%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      4. associate-/l* 50.2%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} \]

   9. Simplified 50.2%

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}} \]

   10. Taylor expanded in y around inf 82.3%

       \[\leadsto \color{blue}{\frac{z}{b}} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-308}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+275}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{1}{t} \cdot \left(y \cdot b\right) + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-119} \lor \neg \left(t \leq 1.66 \cdot 10^{-128}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1e-119) (not (<= t 1.66e-128)))
   (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0)))
   (+ (/ x (+ 1.0 (+ a (* b (/ y t))))) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e-119) || !(t <= 1.66e-128)) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (x / (1.0 + (a + (b * (y / t))))) + (z / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1d-119)) .or. (.not. (t <= 1.66d-128))) then
        tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0d0))
    else
        tmp = (x / (1.0d0 + (a + (b * (y / t))))) + (z / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e-119) || !(t <= 1.66e-128)) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (x / (1.0 + (a + (b * (y / t))))) + (z / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1e-119) or not (t <= 1.66e-128):
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0))
	else:
		tmp = (x / (1.0 + (a + (b * (y / t))))) + (z / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1e-119) || !(t <= 1.66e-128))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t))))) + Float64(z / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1e-119) || ~((t <= 1.66e-128)))
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	else
		tmp = (x / (1.0 + (a + (b * (y / t))))) + (z / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1e-119], N[Not[LessEqual[t, 1.66e-128]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.00000000000000001e-119 or 1.66e-128 < t

   1. Initial program 79.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 83.3%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 89.6%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   if -1.00000000000000001e-119 < t < 1.66e-128

   1. Initial program 62.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 53.0%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 49.0%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 49.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 48.9%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 50.0%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 50.0%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in x around 0 69.0%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}} \]
   8. Step-by-step derivation

      1. +-commutative 69.0%

         \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]

      2. times-frac 57.5%

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{b \cdot y}{t}\right)}} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      3. associate-/l* 53.3%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      4. associate-/l* 53.3%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} \]

   9. Simplified 53.3%

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}} \]

   10. Taylor expanded in y around inf 79.8%

       \[\leadsto \color{blue}{\frac{z}{b}} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-119} \lor \neg \left(t \leq 1.66 \cdot 10^{-128}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{t} + \left(a + 1\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{-119}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t\_1}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-128}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* y (/ b t)) (+ a 1.0))))
   (if (<= t -9e-119)
     (/ (+ x (* y (/ z t))) t_1)
     (if (<= t 1.36e-128)
       (+ (/ x (+ 1.0 (+ a (* b (/ y t))))) (/ z b))
       (/ (+ x (/ y (/ t z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * (b / t)) + (a + 1.0);
	double tmp;
	if (t <= -9e-119) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= 1.36e-128) {
		tmp = (x / (1.0 + (a + (b * (y / t))))) + (z / b);
	} else {
		tmp = (x + (y / (t / z))) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (b / t)) + (a + 1.0d0)
    if (t <= (-9d-119)) then
        tmp = (x + (y * (z / t))) / t_1
    else if (t <= 1.36d-128) then
        tmp = (x / (1.0d0 + (a + (b * (y / t))))) + (z / b)
    else
        tmp = (x + (y / (t / z))) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * (b / t)) + (a + 1.0);
	double tmp;
	if (t <= -9e-119) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= 1.36e-128) {
		tmp = (x / (1.0 + (a + (b * (y / t))))) + (z / b);
	} else {
		tmp = (x + (y / (t / z))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * (b / t)) + (a + 1.0)
	tmp = 0
	if t <= -9e-119:
		tmp = (x + (y * (z / t))) / t_1
	elif t <= 1.36e-128:
		tmp = (x / (1.0 + (a + (b * (y / t))))) + (z / b)
	else:
		tmp = (x + (y / (t / z))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0))
	tmp = 0.0
	if (t <= -9e-119)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_1);
	elseif (t <= 1.36e-128)
		tmp = Float64(Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t))))) + Float64(z / b));
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * (b / t)) + (a + 1.0);
	tmp = 0.0;
	if (t <= -9e-119)
		tmp = (x + (y * (z / t))) / t_1;
	elseif (t <= 1.36e-128)
		tmp = (x / (1.0 + (a + (b * (y / t))))) + (z / b);
	else
		tmp = (x + (y / (t / z))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e-119], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 1.36e-128], N[(N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.0000000000000005e-119

   1. Initial program 78.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 82.9%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 90.8%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   if -9.0000000000000005e-119 < t < 1.36000000000000005e-128

   1. Initial program 62.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 53.0%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 49.0%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 49.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 48.9%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 50.0%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 50.0%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in x around 0 69.0%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}} \]
   8. Step-by-step derivation

      1. +-commutative 69.0%

         \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]

      2. times-frac 57.5%

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{b \cdot y}{t}\right)}} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      3. associate-/l* 53.3%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      4. associate-/l* 53.3%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} \]

   9. Simplified 53.3%

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}} \]

   10. Taylor expanded in y around inf 79.8%

       \[\leadsto \color{blue}{\frac{z}{b}} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} \]

   if 1.36000000000000005e-128 < t

   1. Initial program 81.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 83.6%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 88.5%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 88.5%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 88.6%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 88.6%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 88.6%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-119}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-128}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{if}\;t \leq -4.2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-303}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-28}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) (+ a 1.0))))
   (if (<= t -4.2)
     t_1
     (if (<= t -2.45e-303)
       (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
       (if (<= t 7e-28) (/ (+ z (/ (* x t) y)) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / (a + 1.0);
	double tmp;
	if (t <= -4.2) {
		tmp = t_1;
	} else if (t <= -2.45e-303) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t <= 7e-28) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / (t / z))) / (a + 1.0d0)
    if (t <= (-4.2d0)) then
        tmp = t_1
    else if (t <= (-2.45d-303)) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else if (t <= 7d-28) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / (a + 1.0);
	double tmp;
	if (t <= -4.2) {
		tmp = t_1;
	} else if (t <= -2.45e-303) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t <= 7e-28) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / (a + 1.0)
	tmp = 0
	if t <= -4.2:
		tmp = t_1
	elif t <= -2.45e-303:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	elif t <= 7e-28:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -4.2)
		tmp = t_1;
	elseif (t <= -2.45e-303)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	elseif (t <= 7e-28)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y / (t / z))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -4.2)
		tmp = t_1;
	elseif (t <= -2.45e-303)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	elseif (t <= 7e-28)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2], t$95$1, If[LessEqual[t, -2.45e-303], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-28], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.20000000000000018 or 6.9999999999999999e-28 < t

   1. Initial program 81.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 85.3%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 94.3%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 94.3%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 94.2%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 94.3%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 94.3%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in y around 0 77.4%

      \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{1 + a}} \]

   if -4.20000000000000018 < t < -2.45e-303

   1. Initial program 71.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 69.9%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 66.9%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 66.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 65.0%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}} \]

   6. Taylor expanded in t around 0 75.6%

      \[\leadsto \frac{y \cdot z}{\color{blue}{b \cdot y + t \cdot \left(1 + a\right)}} \]

   if -2.45e-303 < t < 6.9999999999999999e-28

   1. Initial program 63.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 53.0%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 49.6%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 49.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 47.6%

      \[\leadsto \color{blue}{\frac{t \cdot \left(x + \frac{y \cdot z}{t}\right)}{b \cdot y}} \]

   6. Taylor expanded in t around 0 72.4%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t \cdot x}{b \cdot y}} \]
   7. Step-by-step derivation

      1. times-frac 65.3%

         \[\leadsto \frac{z}{b} + \color{blue}{\frac{t}{b} \cdot \frac{x}{y}} \]

   8. Simplified 65.3%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}} \]

   9. Taylor expanded in b around 0 72.4%

      \[\leadsto \color{blue}{\frac{z + \frac{t \cdot x}{y}}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-303}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-28}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+48} \lor \neg \left(t \leq 8.8 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.8e+48) (not (<= t 8.8e-27)))
   (/ (+ x (/ y (/ t z))) (+ a 1.0))
   (+ (/ x (+ 1.0 (+ a (* b (/ y t))))) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.8e+48) || !(t <= 8.8e-27)) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else {
		tmp = (x / (1.0 + (a + (b * (y / t))))) + (z / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.8d+48)) .or. (.not. (t <= 8.8d-27))) then
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    else
        tmp = (x / (1.0d0 + (a + (b * (y / t))))) + (z / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.8e+48) || !(t <= 8.8e-27)) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else {
		tmp = (x / (1.0 + (a + (b * (y / t))))) + (z / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.8e+48) or not (t <= 8.8e-27):
		tmp = (x + (y / (t / z))) / (a + 1.0)
	else:
		tmp = (x / (1.0 + (a + (b * (y / t))))) + (z / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.8e+48) || !(t <= 8.8e-27))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t))))) + Float64(z / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.8e+48) || ~((t <= 8.8e-27)))
		tmp = (x + (y / (t / z))) / (a + 1.0);
	else
		tmp = (x / (1.0 + (a + (b * (y / t))))) + (z / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.8e+48], N[Not[LessEqual[t, 8.8e-27]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.80000000000000012e48 or 8.79999999999999948e-27 < t

   1. Initial program 80.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 85.0%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 94.6%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 94.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 94.6%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 94.6%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 94.6%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in y around 0 78.8%

      \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{1 + a}} \]

   if -2.80000000000000012e48 < t < 8.79999999999999948e-27

   1. Initial program 69.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 64.2%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 61.2%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 61.2%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 61.1%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 61.8%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 61.8%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in x around 0 75.3%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}} \]
   8. Step-by-step derivation

      1. +-commutative 75.3%

         \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]

      2. times-frac 65.0%

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{b \cdot y}{t}\right)}} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      3. associate-/l* 62.5%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      4. associate-/l* 62.5%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} \]

   9. Simplified 62.5%

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}} \]

   10. Taylor expanded in y around inf 73.9%

       \[\leadsto \color{blue}{\frac{z}{b}} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+48} \lor \neg \left(t \leq 8.8 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+48} \lor \neg \left(t \leq 1.8 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{1 + \frac{y \cdot b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.8e+48) (not (<= t 1.8e-29)))
   (/ (+ x (/ y (/ t z))) (+ a 1.0))
   (+ (/ z b) (/ x (+ 1.0 (/ (* y b) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.8e+48) || !(t <= 1.8e-29)) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else {
		tmp = (z / b) + (x / (1.0 + ((y * b) / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.8d+48)) .or. (.not. (t <= 1.8d-29))) then
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    else
        tmp = (z / b) + (x / (1.0d0 + ((y * b) / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.8e+48) || !(t <= 1.8e-29)) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else {
		tmp = (z / b) + (x / (1.0 + ((y * b) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.8e+48) or not (t <= 1.8e-29):
		tmp = (x + (y / (t / z))) / (a + 1.0)
	else:
		tmp = (z / b) + (x / (1.0 + ((y * b) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.8e+48) || !(t <= 1.8e-29))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z / b) + Float64(x / Float64(1.0 + Float64(Float64(y * b) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.8e+48) || ~((t <= 1.8e-29)))
		tmp = (x + (y / (t / z))) / (a + 1.0);
	else
		tmp = (z / b) + (x / (1.0 + ((y * b) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.8e+48], N[Not[LessEqual[t, 1.8e-29]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.80000000000000012e48 or 1.79999999999999987e-29 < t

   1. Initial program 80.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 85.0%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 94.6%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 94.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 94.6%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 94.6%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 94.6%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in y around 0 78.8%

      \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{1 + a}} \]

   if -2.80000000000000012e48 < t < 1.79999999999999987e-29

   1. Initial program 69.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 64.2%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 61.2%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 61.2%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 61.1%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 61.8%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 61.8%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in x around 0 75.3%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}} \]
   8. Step-by-step derivation

      1. +-commutative 75.3%

         \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]

      2. times-frac 65.0%

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{b \cdot y}{t}\right)}} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      3. associate-/l* 62.5%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} + \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)} \]

      4. associate-/l* 62.5%

         \[\leadsto \frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} \]

   9. Simplified 62.5%

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}} \]

   10. Taylor expanded in y around inf 73.9%

       \[\leadsto \color{blue}{\frac{z}{b}} + \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)} \]

   11. Taylor expanded in a around 0 68.6%

       \[\leadsto \frac{z}{b} + \frac{x}{1 + \color{blue}{\frac{b \cdot y}{t}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+48} \lor \neg \left(t \leq 1.8 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{1 + \frac{y \cdot b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -15 \lor \neg \left(t \leq 95000\right):\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -15.0) (not (<= t 95000.0)))
   (/ x (+ 1.0 (+ a (* b (/ y t)))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -15.0) || !(t <= 95000.0)) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-15.0d0)) .or. (.not. (t <= 95000.0d0))) then
        tmp = x / (1.0d0 + (a + (b * (y / t))))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -15.0) || !(t <= 95000.0)) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -15.0) or not (t <= 95000.0):
		tmp = x / (1.0 + (a + (b * (y / t))))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -15.0) || !(t <= 95000.0))
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -15.0) || ~((t <= 95000.0)))
		tmp = x / (1.0 + (a + (b * (y / t))));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -15.0], N[Not[LessEqual[t, 95000.0]], $MachinePrecision]], N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -15 or 95000 < t

   1. Initial program 81.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 86.1%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 96.0%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 96.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 95.9%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 96.0%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 96.0%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in x around inf 65.8%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]
   8. Step-by-step derivation

      1. associate-/l* 70.5%

         \[\leadsto \frac{x}{1 + \left(a + \color{blue}{b \cdot \frac{y}{t}}\right)} \]

   9. Simplified 70.5%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}} \]

   if -15 < t < 95000

   1. Initial program 68.7%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 63.8%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 60.9%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 47.3%

      \[\leadsto \color{blue}{\frac{t \cdot \left(x + \frac{y \cdot z}{t}\right)}{b \cdot y}} \]

   6. Taylor expanded in t around 0 66.0%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t \cdot x}{b \cdot y}} \]
   7. Step-by-step derivation

      1. times-frac 63.8%

         \[\leadsto \frac{z}{b} + \color{blue}{\frac{t}{b} \cdot \frac{x}{y}} \]

   8. Simplified 63.8%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}} \]

   9. Taylor expanded in b around 0 66.8%

      \[\leadsto \color{blue}{\frac{z + \frac{t \cdot x}{y}}{b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -15 \lor \neg \left(t \leq 95000\right):\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \lor \neg \left(t \leq 3 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.2) (not (<= t 3e-29)))
   (/ (+ x (* y (/ z t))) (+ a 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.2) || !(t <= 3e-29)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-6.2d0)) .or. (.not. (t <= 3d-29))) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.2) || !(t <= 3e-29)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.2) or not (t <= 3e-29):
		tmp = (x + (y * (z / t))) / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.2) || !(t <= 3e-29))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -6.2) || ~((t <= 3e-29)))
		tmp = (x + (y * (z / t))) / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.2], N[Not[LessEqual[t, 3e-29]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.20000000000000018 or 3.0000000000000003e-29 < t

   1. Initial program 81.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 85.3%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 94.3%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 94.3%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.4%

      \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\color{blue}{1 + a}} \]

   if -6.20000000000000018 < t < 3.0000000000000003e-29

   1. Initial program 67.7%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 62.2%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 59.1%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 59.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 49.7%

      \[\leadsto \color{blue}{\frac{t \cdot \left(x + \frac{y \cdot z}{t}\right)}{b \cdot y}} \]

   6. Taylor expanded in t around 0 69.1%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t \cdot x}{b \cdot y}} \]
   7. Step-by-step derivation

      1. times-frac 66.0%

         \[\leadsto \frac{z}{b} + \color{blue}{\frac{t}{b} \cdot \frac{x}{y}} \]

   8. Simplified 66.0%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}} \]

   9. Taylor expanded in b around 0 69.2%

      \[\leadsto \color{blue}{\frac{z + \frac{t \cdot x}{y}}{b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \lor \neg \left(t \leq 3 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \lor \neg \left(t \leq 4 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.5) (not (<= t 4e-26)))
   (/ (+ x (/ y (/ t z))) (+ a 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.5) || !(t <= 4e-26)) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.5d0)) .or. (.not. (t <= 4d-26))) then
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.5) || !(t <= 4e-26)) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.5) or not (t <= 4e-26):
		tmp = (x + (y / (t / z))) / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.5) || !(t <= 4e-26))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.5) || ~((t <= 4e-26)))
		tmp = (x + (y / (t / z))) / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.5], N[Not[LessEqual[t, 4e-26]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5 or 4.0000000000000002e-26 < t

   1. Initial program 81.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 85.3%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 94.3%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 94.3%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 94.2%

         \[\leadsto \frac{x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

      2. un-div-inv 94.3%

         \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   6. Applied egg-rr 94.3%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]

   7. Taylor expanded in y around 0 77.4%

      \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{1 + a}} \]

   if -4.5 < t < 4.0000000000000002e-26

   1. Initial program 67.7%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 62.2%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 59.1%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 59.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 49.7%

      \[\leadsto \color{blue}{\frac{t \cdot \left(x + \frac{y \cdot z}{t}\right)}{b \cdot y}} \]

   6. Taylor expanded in t around 0 69.1%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t \cdot x}{b \cdot y}} \]
   7. Step-by-step derivation

      1. times-frac 66.0%

         \[\leadsto \frac{z}{b} + \color{blue}{\frac{t}{b} \cdot \frac{x}{y}} \]

   8. Simplified 66.0%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}} \]

   9. Taylor expanded in b around 0 69.2%

      \[\leadsto \color{blue}{\frac{z + \frac{t \cdot x}{y}}{b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \lor \neg \left(t \leq 4 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -950 \lor \neg \left(t \leq 115000\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -950.0) (not (<= t 115000.0)))
   (/ x (+ a 1.0))
   (/ (+ z (* t (/ x y))) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -950.0) || !(t <= 115000.0)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + (t * (x / y))) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-950.0d0)) .or. (.not. (t <= 115000.0d0))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = (z + (t * (x / y))) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -950.0) || !(t <= 115000.0)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + (t * (x / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -950.0) or not (t <= 115000.0):
		tmp = x / (a + 1.0)
	else:
		tmp = (z + (t * (x / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -950.0) || !(t <= 115000.0))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -950.0) || ~((t <= 115000.0)))
		tmp = x / (a + 1.0);
	else
		tmp = (z + (t * (x / y))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -950.0], N[Not[LessEqual[t, 115000.0]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -950 or 115000 < t

   1. Initial program 81.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 86.1%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 96.0%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 96.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 61.9%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   if -950 < t < 115000

   1. Initial program 68.7%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 63.8%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 60.9%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 47.3%

      \[\leadsto \color{blue}{\frac{t \cdot \left(x + \frac{y \cdot z}{t}\right)}{b \cdot y}} \]

   6. Taylor expanded in t around 0 66.0%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t \cdot x}{b \cdot y}} \]
   7. Step-by-step derivation

      1. times-frac 63.8%

         \[\leadsto \frac{z}{b} + \color{blue}{\frac{t}{b} \cdot \frac{x}{y}} \]

   8. Simplified 63.8%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}} \]

   9. Taylor expanded in b around 0 66.8%

      \[\leadsto \color{blue}{\frac{z + \frac{t \cdot x}{y}}{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 65.3%

          \[\leadsto \frac{z + \color{blue}{t \cdot \frac{x}{y}}}{b} \]

   11. Simplified 65.3%

       \[\leadsto \color{blue}{\frac{z + t \cdot \frac{x}{y}}{b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -950 \lor \neg \left(t \leq 115000\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -52 \lor \neg \left(t \leq 96000\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -52.0) (not (<= t 96000.0)))
   (/ x (+ a 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -52.0) || !(t <= 96000.0)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-52.0d0)) .or. (.not. (t <= 96000.0d0))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -52.0) || !(t <= 96000.0)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -52.0) or not (t <= 96000.0):
		tmp = x / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -52.0) || !(t <= 96000.0))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -52.0) || ~((t <= 96000.0)))
		tmp = x / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -52.0], N[Not[LessEqual[t, 96000.0]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -52 or 96000 < t

   1. Initial program 81.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 86.1%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 96.0%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 96.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 61.9%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   if -52 < t < 96000

   1. Initial program 68.7%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 63.8%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 60.9%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 47.3%

      \[\leadsto \color{blue}{\frac{t \cdot \left(x + \frac{y \cdot z}{t}\right)}{b \cdot y}} \]

   6. Taylor expanded in t around 0 66.0%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t \cdot x}{b \cdot y}} \]
   7. Step-by-step derivation

      1. times-frac 63.8%

         \[\leadsto \frac{z}{b} + \color{blue}{\frac{t}{b} \cdot \frac{x}{y}} \]

   8. Simplified 63.8%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}} \]

   9. Taylor expanded in b around 0 66.8%

      \[\leadsto \color{blue}{\frac{z + \frac{t \cdot x}{y}}{b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -52 \lor \neg \left(t \leq 96000\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -55 \lor \neg \left(t \leq 3.9 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -55.0) (not (<= t 3.9e-30))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -55.0) || !(t <= 3.9e-30)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-55.0d0)) .or. (.not. (t <= 3.9d-30))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -55.0) || !(t <= 3.9e-30)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -55.0) or not (t <= 3.9e-30):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -55.0) || !(t <= 3.9e-30))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -55.0) || ~((t <= 3.9e-30)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -55.0], N[Not[LessEqual[t, 3.9e-30]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -55 or 3.9000000000000003e-30 < t

   1. Initial program 81.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 85.3%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 94.3%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 94.3%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 58.6%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   if -55 < t < 3.9000000000000003e-30

   1. Initial program 67.7%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 62.2%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 59.1%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 59.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 58.8%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -55 \lor \neg \left(t \leq 3.9 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 40.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.8e+149) x (if (<= t 2e+19) (/ z b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.8e+149) {
		tmp = x;
	} else if (t <= 2e+19) {
		tmp = z / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-6.8d+149)) then
        tmp = x
    else if (t <= 2d+19) then
        tmp = z / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.8e+149) {
		tmp = x;
	} else if (t <= 2e+19) {
		tmp = z / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.8e+149:
		tmp = x
	elif t <= 2e+19:
		tmp = z / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.8e+149)
		tmp = x;
	elseif (t <= 2e+19)
		tmp = Float64(z / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6.8e+149)
		tmp = x;
	elseif (t <= 2e+19)
		tmp = z / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.8e+149], x, If[LessEqual[t, 2e+19], N[(z / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -6.7999999999999997e149 or 2e19 < t

   1. Initial program 80.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 85.0%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 97.7%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 65.5%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   6. Taylor expanded in a around 0 36.2%

      \[\leadsto \color{blue}{x} \]

   if -6.7999999999999997e149 < t < 2e19

   1. Initial program 71.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 69.1%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 67.4%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 50.3%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 40.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+149}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.5e+149) (- x (* x a)) (if (<= t 4.5e+20) (/ z b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.5e+149) {
		tmp = x - (x * a);
	} else if (t <= 4.5e+20) {
		tmp = z / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-6.5d+149)) then
        tmp = x - (x * a)
    else if (t <= 4.5d+20) then
        tmp = z / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.5e+149) {
		tmp = x - (x * a);
	} else if (t <= 4.5e+20) {
		tmp = z / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.5e+149:
		tmp = x - (x * a)
	elif t <= 4.5e+20:
		tmp = z / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.5e+149)
		tmp = Float64(x - Float64(x * a));
	elseif (t <= 4.5e+20)
		tmp = Float64(z / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6.5e+149)
		tmp = x - (x * a);
	elseif (t <= 4.5e+20)
		tmp = z / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.5e+149], N[(x - N[(x * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+20], N[(z / b), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if t < -6.50000000000000015e149

   1. Initial program 72.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 79.7%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 99.8%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 66.1%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   6. Taylor expanded in a around 0 35.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot x\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 35.4%

         \[\leadsto x + \color{blue}{\left(-a \cdot x\right)} \]

      2. unsub-neg 35.4%

         \[\leadsto \color{blue}{x - a \cdot x} \]

   8. Simplified 35.4%

      \[\leadsto \color{blue}{x - a \cdot x} \]

   if -6.50000000000000015e149 < t < 4.5e20

   1. Initial program 71.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 69.1%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 67.4%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 50.3%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if 4.5e20 < t

   1. Initial program 84.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 87.5%

         \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. associate-/l* 96.7%

         \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 65.2%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   6. Taylor expanded in a around 0 36.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+149}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 19.6% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 74.9%

   \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
2. Step-by-step derivation

   1. associate-/l* 74.7%

      \[\leadsto \frac{x + \color{blue}{y \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. associate-/l* 78.2%

      \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \color{blue}{y \cdot \frac{b}{t}}} \]

3. Simplified 78.2%

   \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 41.1%

   \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

6. Taylor expanded in a around 0 19.0%

   \[\leadsto \color{blue}{x} \]

7. Final simplification 19.0%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 79.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))
   (if (< t -1.3659085366310088e-271)
     t_1
     (if (< t 3.036967103737246e-130) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 * ((x + ((y / t) * z)) * (1.0d0 / ((a + 1.0d0) + ((y / t) * b))))
    if (t < (-1.3659085366310088d-271)) then
        tmp = t_1
    else if (t < 3.036967103737246d-130) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))))
	tmp = 0
	if t < -1.3659085366310088e-271:
		tmp = t_1
	elif t < 3.036967103737246e-130:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 * Float64(Float64(x + Float64(Float64(y / t) * z)) * Float64(1.0 / Float64(Float64(a + 1.0) + Float64(Float64(y / t) * b)))))
	tmp = 0.0
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	tmp = 0.0;
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 * N[(N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.3659085366310088e-271], t$95$1, If[Less[t, 3.036967103737246e-130], N[(z / b), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))